Monday, October 8, 2012 - 14:00 , Location: 005 , Xiaobing Feng , University of Tennessee , Organizer: Haomin Zhou
In this talk I shall present some latest advances on developing numerical methods (such as finite difference methods, Galerkin methods, discontinuous Galerkin methods) for fully nonlinear second order PDEs including Monge-Ampere type equations and Hamilton-Jacobi-Bellman equations. The focus of this talk is to present a new framework for constructing finite difference methods which can reliably approximate viscosity solutions of these fully nonlinear PDEs. The connection between this new framework with the well-known finite difference theory for first order fully nonlinear Hamilton-Jacobi equations will be explained. Extensions of these finite difference techniques to discontinuous Galerkin settings will also be discussed.
Monday, October 1, 2012 - 14:00 , Location: Skiles 005 , Martin Short , UCLA Math department , Organizer: Luca Dieci
In this era of "big data", Mathematics as it applies to human behavior is becoming a much more relevant and penetrable topic of research. This holds true even for some of the less desirable forms of human behavior, such as crime. In this talk, I will discuss the mathematical modeling of crime on two different "scales", as well as the results of experiments that are being performed to test the usefulness and accuracy of these models. First, I will present a data-driven model of crime hotspots at the scale of neighborhoods -- adapted from literature on earthquake predictions -- along with the results of this model's application within the LAPD. Second, I will describe a game-theoretic model of crime and punishment at the scale of a society, and compare the model to results of lab-based economic experiments performed by myself and collaborators.
Monday, September 10, 2012 - 14:00 , Location: Skiles 005 , Xiaoqiang Wang , Department of Scientific Computing, Florida State University , email@example.com , Organizer: Sung Ha Kang
[This talk is canceled. Sep 9, 2012 ] Centroidal Voronoi Tessellations(CVTs) are special Voronoi Tessellations where the centroidal of each segments coincides with its Voronoi generators. CVT has broad applications in various fields. In this talk, we will present a new development for CVT algorithms, Edge-weighted CVTs, which puts the segment boundary length information to the consideration of CVT algorithms. We will demonstrate how EWCVTs can be applied in image segmentations, superpixels, etc.
Monday, August 27, 2012 - 14:00 , Location: Skiles 005 , Bruce A. Wade , Department of Mathematical Sciences, University of Wisconsin-Milwaukee , Organizer: Yingjie Liu
We discuss various exponential time differencing (ETD) schemes designed to handle nonlinear parabolic systems. The ETD schemes use certain Pade approximations of the matrix exponential function. These ETD schemes have potential to be implemented in parallel and their performance is very robust with respect to the type of PDE. They are unconditionally stable and computationally very fast due to the technique of computing the nonlinear part explicitly. To handle the problem of irregular initial or boundary data an adaptive ETD scheme is utilized, which adds sufficient damping of spurious oscillations. We discuss algorithm development, theory and applications.
Compact Numerical Quadrature Formulas for Singular and Hypersingular Integrals and Integral EquationsMonday, August 20, 2012 - 14:00 , Location: Skiles 005 , Prof. Avram Sidi , Technion - Israel Institute of Technology , firstname.lastname@example.org , Organizer: Haomin Zhou
Wednesday, June 13, 2012 - 11:00 , Location: Skiles 255 , Minh Ha-Quang , Italian Institute of Technology , Organizer: Sung Ha Kang
Slow Feature Analysis (SFA) is a method for extracting slowly varying features from input signals. In this talk, we generalize SFA to vector-valued functions of multivariables and apply it to the problem of blind source separation, in particular image separation. When the sources are correlated, we apply the following technique called decorrelation filtering: use a linear filter to decorrelate the sources and their derivatives, then apply the separating matrix obtained on the filtered sources to the original sources. We show that if the filtered sources are perfectly separated by this matrix, then so are the original sources.We show how to numerically obtain such a decorrelation filter by solving a nonlinear optimization problem. This technique can also be applied to other linear separation methods, whose output signals are uncorrelated, such as ICA.This is joint work with Laurenz Wiskott (Proceedings of the 13th IEEE International Conference in Computer Vision, ICCV 2011, Barcelona, Spain).
Friday, May 18, 2012 - 14:05 , Location: 006 Skiles , Ke Chen , University of Liverpool , Organizer: Haomin Zhou
Both segmentation and registration are important image processing tasks in a number of real life applications. While there exist powerful and effective models,many scientific challenges remain open. In this talk, I shall first present some image segmentation work of modelsand algorithms in two and three dimensions, followed by some recent works of selective segmentationThen I introduce some new work on multimodality image registration modelling.Numerical experiments will demonstrate the advantages of our new models and algorithms over existing results. Collaborators related to this work include Noor Badshah (Peshawar, Pakistan), Jian-ping Zhang and Bo Yu (Dalian, China),Lavdie Rada (Liverpool), C Brito (Mexico) and N Chumchob (Thailand).
Monday, April 23, 2012 - 14:00 , Location: Skiles 006 , Fangxu Jing , GT Math , Organizer:
We analyze two-link (or three-link) 2D snake like locomotions and discuss the optimization of the motion. The snake is modeled as two (or three) identical links connected via hinge joints and the relative angles between the links are prescribed as periodic actuation functions. An essential feature of the locomotion is the anisotropy of friction coefficients. The dynamics of the snake is analyzed numerically, as well as analytically for small amplitude actuations of the relative angles. Cost of locomotion is defined as the ratio between distance traveled by the snake and the energy expenditure within one period. Optimal conditions of the highest efficiency in terms of the friction coefficients and the actuations are discussed for the model.
Monday, April 16, 2012 - 14:00 , Location: Skiles 006 , Margaret Cheney , Rensselaer Polytechnic Institute , Organizer: Haomin Zhou
Radar imaging is a technology that has been developed, verysuccessfully, within the engineering community during the last 50years. Radar systems on satellites now make beautiful images ofregions of our earth and of other planets such as Venus. One of thekey components of this impressive technology is mathematics, and manyof the open problems are mathematical ones.This lecture will explain, from first principles, some of the basicsof radar and the mathematics involved in producing high-resolutionradar images.
Monday, April 9, 2012 - 14:00 , Location: Skiles 006 , Xiaolin Wang , GT Math , Organizer:
The Glezer lab at Georgia Tech has found that vorticity can improve heat transfer efficiency in electronic hardware. Vortices are able to enhance the forced convection in the boundary layer and fully mix the heated fluid with cooler core flow. Some recent experiments showed the possibility of using a vibrated reed to produce vortices in heat sinks. In this work, we simulate both the fluid and the heat transfer process in a 3-dimensional plate fin heat sink. We propose a simplified model by considering flow and temperature in a 2-D channel, and extend the model to the third dimension using a 1-D heat fin model. We simulate periodically steady-state solutions. We show that the total heat flux transferred from the plate to the fluid can be improved with vortices given the same input power. A possible optimal solution for the largest heat transfer efficiency is proposed for the physical parameters of a real computer heat sink. We discuss the effect of the important parameters such as Reynolds number and thermal conductivities.